模糊收敛群及其在粗糙集中的应用

This project is devoted to incorporating group into fuzzy convergence space,and so fuzzy convergence group is topologically much better than fuzzy convergence space.The project is arranged as follows:. Firstly, various definitions of fuzzy convergence space are considered, and their relationships are revealed. Further, the suitable framework for this project is established.. Secondly, based on categorical theory and Cauchy filters in fuzzy convergence group, the relationships between fuzzy convergence group, fuzzy Cauchy group and fuzzy topology group are established. Based on these facts, the completions of fuzzy Cauchy group, fuzzy convergence group, and fuzzy topology group are considered.. Lastly, the application of fuzzy convergence group is considered.With the help of generated subgroup and fuzzy set extension, a method of the recovery information on rough set is obtained.

本项目旨在把群运算融入模糊收敛空间，以提升模糊收敛空间的拓扑性质。首先，整合模糊收敛空间的多种定义，揭示它们之间的联系，进而为本项目找到一个合适的框架，使得在这个框架下项目的关键问题顺利解决。其次，利用代数理论和范畴论，并借助于柯西滤子，建立模糊收敛群、模糊柯西群和模糊拓扑群的联系，在此基础上，给出它们的完备化形式。最后，讨论了模糊收敛群在粗糙集理论中的应用，利用生成子群和模糊集扩张原理，得到一种在粗糙集理论中信息恢复的方法。

本项目旨在把群运算融入到模糊收敛空间和模糊拓扑空间(一类特殊的模糊收敛空间)，以提升这些空间的性质，并给出在粗糙集方面的应用。该项目研究了模糊收敛空间的一些质，给出了这些空间和其他空间的联系。在此基础上，把群运算引入到模糊收敛空间，建立了模糊收敛群和模糊柯西群的联系。最后从序和模糊拓扑的角度研究了粗糙集理论，并给出了相关的应用。